The latest version of the draft, first proposed in the 15-nation council last Thursday, added several provisions in an attempt to win broader support, after some members criticised the text as biased against Israel.
However, John Bolton, the US ambassador to the UN, said it remained flawed and that Washington still saw no need for council action.
The initial draft, put forward by Qatar, the council's sole Arab member, on behalf of Arab, Islamic and non-aligned states at the UN, condemned Israel's arrest and detention of dozens of elected Palestinian officials.
It also decried the "large-scale military assault" in Gaza launched after Palestinian fighters captured Corporal Gilad Shalit on June 25, and demanded that Israel "immediately cease its aggression" against Palestinian civilians, pull its forces out of Gaza and release the detained Palestinian officials.
The new draft added language expressing "grave concern" about the firing of rockets from Gaza into Israel and condemning "all acts of violence, terror and destruction", including the recent abduction and killing of an Israeli civilian in the West Bank.
It called on the Palestinian Authority to "take immediate and sustained action to bring an end to violence, including the firing of rockets on Israeli territory" and for emergency aid to be provided for the Palestinian people.
Junior council diplomats met on Tuesday afternoon to revise the text and suggest further changes.
However, Bolton told reporters that US still considered the draft resolution as "unsatisfactory".
Asked if Washington, Israel's closest ally, would exercise its veto if the measure were brought to a vote, he responded: "Our position remains the same, that we don't see at this point any utility in council action at all."
Israel has expanded its two-week offensive aimed at recovering the captured soldier and has vowed to continue the offensive indefinitely, rejecting broad international criticism of its biggest operation in Gaza since withdrawing from the territory last year.